# zhptri (3) - Linux Manuals

zhptri.f -

## SYNOPSIS

### Functions/Subroutines

subroutine zhptri (UPLO, N, AP, IPIV, WORK, INFO)
ZHPTRI

## Function/Subroutine Documentation

### subroutine zhptri (characterUPLO, integerN, complex*16, dimension( * )AP, integer, dimension( * )IPIV, complex*16, dimension( * )WORK, integerINFO)

ZHPTRI

Purpose:

``` ZHPTRI computes the inverse of a complex Hermitian indefinite matrix
A in packed storage using the factorization A = U*D*U**H or
A = L*D*L**H computed by ZHPTRF.
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U':  Upper triangular, form is A = U*D*U**H;
= 'L':  Lower triangular, form is A = L*D*L**H.
```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.
```

AP

```          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by ZHPTRF,
stored as a packed triangular matrix.

On exit, if INFO = 0, the (Hermitian) inverse of the original
matrix, stored as a packed triangular matrix. The j-th column
of inv(A) is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
```

IPIV

```          IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHPTRF.
```

WORK

```          WORK is COMPLEX*16 array, dimension (N)
```

INFO

```          INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley